So again, it sounds pretty close to 8000 rpm. It's way better than a guess.

Fantastic idea! Taking your lead I dove in head first.

I began testing a couple of dyno recordings and fairly quickly found an E92 M3 video and V12 Aston with 6800 rpm redline. I recorded the sounds (just from crappy Youtube videos) and then did a Fourier transform to get the spectral content. E92 M3 frequency peak at redline should be 560 Hz, I measured 570 Hz. V12 Aston is 680 Hz theoretical, 688 observed. In both cases "the" peak was actually the second peak not the first. Those results are within about 2%. The method absolutely can work.

Moving on the the M4 video I'm not entirely sure that around the 3:07 time mark he get's a true redline shift. I think this is at Galgenkopf, what do you think? Based on that he is indeed most likely in 3rd and I agree that the peak speed at redline should be around 90-97 mph (depending both on gearing and redline). Getting a true discernible peak in the spectral results was not straight forward as compared to the dyno runs (to be expected) and thus my results are a range of frequencies from 345-365 Hz. The capture below from ~5.5-6.0 seconds is showing a discernible (first) peak at 358 Hz. Combining that with the Doppler effect from 90-97 mph gives a source frequency in the range of about 385 - 415 Hz. That in turn translates to 7700-8300 rpm! This is entirely consistent with my prior estimate of a peak redline of 7700 rpm.

UPDATE 7/26: Thanks to some additional insights from post below by bradleyland I am revising my final rpm estimate down considerably to 7250-7550 rpm. In short my audio capture was too low in quality. I did recheck a couple cases of dynos mentioned above using the new technique. For instance the V12 Aston came in at 6770 vs. 6800 quoted, less than 0.5% difference.

Given the F10 M5s redline in particular, 7200 rpm, I just don't think 8000 (Admin edit:rumor is close to 8000 rpm) is possible. There is also the prior problem of resolving the inconsistency of an 8000 rpm redline, about 400 ft lb of torque and about the same power as the existing M3...

To be more accurate and more certain we need a video of a clear redline shift with good audio quality and minimal Doppler (i.e. camera right by shift point). Anyone?

Swamp, if you were my professor I would love your lectures but loathe your exams. That's very impressive work - gotta give props to both you and the guy that suggested the idea. I'll be even more impressed if your numbers match the production engine.

I wonder if the engine sounds from development-M5 track footage consistently yield 7200RPM. It would be an example (or examples) that are close to home.

Swamp, if you were my professor I would love your lectures but loathe your exams. That's very impressive work - gotta give props to both you and the guy that suggested the idea. I'll be even more impressed if your numbers match the production engine.

I wonder if the engine sounds from development-M5 track footage condisently yield 7200RPM. It would be an example (or examples) that are close to home.

Thanks. I wanted to do some more work using actual track clips but did not have the chance. If you can suggest a good, clear redline occurrence for the F10 M5 I would be happy to repeat the analysis. It very quick to do actually, the software does everything.

I'm no expert in this field, but aren't there still a number of unknowns you'd need to know before making these calculations? I see you make an estimate on speed, but wouldn't gearing and exhaust acoustics also come into play? Also, it's probably a safe assumption, but still an assumption that the car is shifting at redline.